00:02
Okay, hello. I'm Cailin O'Connor from the Department of Logic and Philosophy of Science at UC Irvine. And the talk I'll be giving is measuring conventionality. I'm really pleased to be part of this seminar series, and I will just jump in.

00:20
Alright, so there are a lot of different conventions in human societies. To give a very classic example, in some countries like in the US people drive on the right side of the road. In other countries like India and Australia, they drive on the left side of the road. There are a lot of debates in philosophy about what conventions are, but people can generally agree that they involve stable, possibly beneficial patterns of social behaviour. And, furthermore, that these behaviours are arbitrary—in the sense that they could have been otherwise. So that's a really important part of typical definitions of conventions.

01:04
So my aim in this talk is going to be to do two things. So first of all, to argue for a conception of conventions as coming in degrees of arbitrariness, rather than as being "either/or" types of things. And second, to give a measure for this arbitrariness. And I have an aim here, which is to improve cultural evolutionary explanations.

01:32
So in general, I think cultural traits should be explained, or should not be explained as either functional or as arbitrary—but they're almost always both. And I think the framework I developed here will give us language to talk about the degrees to which they are functional, arbitrary, or somewhere along some range in between these.

01:55
Alright, here's a roadmap for the rest of the talk. So first, I'll talk about a couple philosophical accounts of what conventionality is; accounts that are relevant to the framework I'm developing here. Second, I'll talk a bit about evolutionary models of cultural traits. And that will set us up for part three, where I do sort of the main thing I'm doing, which is to describe this measure of the arbitrariness of different conventions. Now, I won't actually do part four of the talk, where I give examples of applying this measure and trying to use it to improve cultural evolutionary explanation for time purposes. But I left this here to flag that I've got that part of this project. And if anyone's interested, there's actually a paper associated with this talk, which can be found on my website, or you can email me for it.

02:48
Okay, so I take David Lewis's account of convention to still be the received view and philosophy. So he really developed this in the book Convention, which came out I believe, in 1970. What he does there is describe conventions as a sort of equilibrium in a coordination game. And the idea is that you have a sort of coordination scenario: you have a group of people engaged in the scenario, most members of the group are adhering to an equilibrium behaviour, they're expecting others to adhere to it, and they prefer to do so if others do. And he has a whole list of very detailed requirements here. So I won't go into the details. But this is the general picture.

03:32
So what does he mean by a coordination game? Well, here's what's called a payoff table for a game. So this is a model of a scenario where you have two individuals who want to coordinate their behaviour by doing the same thing. And they can get some kind of payoff by doing that. But there are multiple different ways they can do that. So in this case, there are two. So in this game, we have two players, player one, player two. They each have two actions, they could take A or B, A or B. And if they both take the same action, they get a payoff of one. So player one's payoffs are listed first and player two second. So they can get good payoffs in these two ways. But if they miscoordinate, they get a payoff of zero. And this could represent something like the decision to drive on the right or left side of the road. People don't actually care very much which side of the road they drive on, but they both want to drive on the same side—and if they don't, they get poor payoffs. So in this game, we have two equilibria of the game, both playing a and both playing B. And those would be for David Lewis, two possible conventions you might have in this sort of coordination scenario. So he sets this up as a way to define what things are conventions or aren't.

04:49
Now, Margaret Gilbert brings a lot of criticisms to bear on Lewis. Here's one she points out; that there are games which are going to fall under his definition, but where the conventionality of a convention seems attenuated. So suppose we have this kind of coordination scenario, but one of the outcomes yields a much better payoff say that they get a payoff of 100. If they take the B outcome rather than the A outcome. Well, if they end up at B, you might say, is that really a convention? It doesn't seem like it really could have been otherwise. And Lewis's response is something like, well, in these cases, you don't really have an appropriate alternative to B, because you can't generate common knowledge that everyone would be doing the A convention, because the payoffs are so poor. So he says, Well, this is a case where the other convention is really a deficient one, so it doesn't count.

05:46
But the thing is, there's going to be a whole scale of cases, going from a situation where x equals one, to two conventions are equally good, to a situation where one is much better. And it seems strange to say that somewhere in there on that scale, we go from situations where there are conventions to situations where they're not, rather than saying we just have different degrees here of conventionality, or degrees of arbitrariness or could have been otherwise.

06:16
I'll bring up one more sort of relevant point here. So Ruth Millikan does work on convention as well. And her definition of it, which is driven by examples related to semantic meaning, includes a requirement that if something's a convention, it should be unlikely to emerge a second time. So if we roll back the cultural evolutionary tape and start again, we shouldn't get the same thing again.

06:41
But that actually excludes Lewis's core cases where you have two possibilities, because you know, if we think about this kind of case, absent other factors, we might say, well, there's a 50/50 chance that we get the same convention emerging again. And we can contrast that to cases where there might be a lot of possible equilibria. So if we think about, you know, the meaning of the word, fork, there are an indefinite number of possible equilibria. There, and it is quite unlikely that the same one would emerge a second time. So again, we might want to say we could scale between cases where there are very few possible conventions that could emerge, and a lot of them and in that latter case, maybe they're more arbitrary, or there's a greater sense in which they could have been otherwise.

07:29
Now, driven by concerns like these, Mandy Simons and Kevin Zollman in a recent paper give an account in which they want to think about conventions as being more or less natural versus arbitrary. And they give three senses in which this could be so they say, Well, sometimes we have conventions that are better from a payoff standpoint, and that's similar to the Gilbert example. They say, in some cases, we have conventions that are more likely to emerge than others. And they say, in some cases, we have conventions that are more stable than others—they're unlikely to be abandoned. And they want to say these types of conventions with higher payoffs more likely to emerge and more stable, are more natural compared to other more, you know, arbitrary, or less natural types of conventions. Now, in this talk, I am going to really make use of this sort of second notion as the one I'm interested in, in thinking about cases in which conventions are more or less arbitrary: how likely is it that a convention emerges, and to what degree could it really be the case that something else emerges, will be the sense that I'm focused on here in this framework I'm building.

08:50
So with that, let's move on to evolutionary models of cultural traits. And the reason I'm going to do this will become clear in section three, where I'm sort of outlining my measure, is that these models give a really good way to talk about the sort of arbitrariness of conventions and the chances that they could have been otherwise. Alright, so here's a kind of general framework for understanding cultural evolutionary models and how they work. So they usually involve, first of all, a population with different possible variants or strategies. So these strategies could be drive on the right or the left side of the road, they could be many other types of behaviours. That could be part of a convention. The models usually involve repeated interactions over time. So you have individuals modelled, who are engaged in some sort of social interactions, and then they also involve rules for change. These are called dynamics, and these rules stipulate how these variants are going to change based on the interactions that the agents or the represented individuals in the model undergo. And typically what happens.

10:05
So you have a population with these different variants. It's evolving according to dynamics. And usually models end up at what are called equilibria. And equilibria in these models are usually stable: they represent stable—sometimes beneficial, depending on the model, but often beneficial—states that typically could have been otherwise. So in other words, cultural evolutionary models often are good representations of the emergence of conventions or things that we might think of as conventions.

10:38
All right, so let's consider this game that comes from Lewis that is kind of this very basic coordination game. So this is now just kind of an example to show how this kind of model might go. And let's say, we have a model where we have individuals playing this game, and this population evolves according to a very standard dynamics that assumes that when you have individuals who strategies get good payoffs, those strategies tend to spread, and those with poor strategies tend to contract.

11:13
So notice here we have two equilibria, which are these two kind of conventions for Lewis coordination on the A strategy and the B. But we'll say there could be different payoffs for one of these equilibria, the B strategy could be just as good as A or it could be much better, or it could be worse.

11:32
All right. So what I'm showing here are called phase diagrams. So this is what's called the phase diagram for the model where the two equilibria are equally good, where x equals one. So what this is showing is all the different possible population states: you could have in this model from everyone in the population playing B to everyone in the population playing A, and what the arrows show is how the population changes at different points based on these distributions. And what we see here is we have these two equilibria, everyone doing A and everyone doing B. And whenever we have the population in another state, it's changing so that it moves towards the more common equilibria. So if there are more a people, it moves towards a, if there's more B people, it moves towards B. And the reason for that is that this is a coordination game. So the people who are doing the more common thing tend to coordinate, they get better payoffs, the population evolves in that direction.

12:34
I also show here a phase diagram for the same model, but where X equals 50. So now we have a much better equilibrium. And as we can see, here, we have the same basic structure: when there's a lot of A's it goes to A when there's more B's, it goes to B. But now we need a much smaller number of B's to get the whole population moving that way. Because when you get a high payoff for coordinating with B, you only need to coordinate a little bit at a time for that to be the better strategy.

13:02
So we have these two kind of evolving systems. And we've analysed what will happen for different population states and both of them. One thing we can now define for these models are what are called basins of attraction. So for any equilibria, a basin of attraction is the set of states that's going to evolve to that one. And what we can see here is we have two basins of attraction and they're equally sized. Whereas in this model, we have two basins of attraction and one of them is much larger than the other. So there are many more initial states that will move towards the B equilibrium.

13:38
So notice here, this corresponds to this sense of naturalness from Simons and Zollman that I said I'm going to focus on; where we have one equilibrium that has a greater likelihood of emergence. They might say it's more natural, because it's more likely to emerge. I might say something like, if we find ourselves at this equilibrium, we might say, well, there's not a very strong sense in which it could have been otherwise because this is such a likely outcome.

14:08
Okay, so now let's talk about the measure. So I'm not going to prevent present a measure of the arbitrariness of conventions. What I'm going to do here is draw on information theory. So this is the theory that addresses questions related to the transfer of information. So what's the connection? Well, we have a scenario where you can have different equilibria with different probabilities of emerging basins of attraction is one way to represent this. These probabilities determine how much we learn or how much information we gain when we see what evolved. And that level is going to be our measure: how surprised are we when we discover what equilibrium actually emerged in a culturally evolving scenario, and that tells us about how much that equilibrium really could have been otherwise.

15:05
So in particular, the measure I use is called Shannon entropy. So, in information theory, entropy measures the following thing: you have some channel, where information can flow through it. The expected amount of information that you're on average going to have coming through a channel is its entropy. So by a channel here, I mean, basically, any variable that can be in multiple states and can convey information that way. So it could be a stoplight that's either red, yellow, or green. And then the messages coming through it are either red, yellow, or green. And you can ask, how much information do I get on average, when I observe what state the stoplight is in?

15:46
So entropy, this might look like a complicated equation, but its not—it's a weighted average. It averages over all your possible messages: what's the probability of the message times the amount of information that message carries. So it just takes the different states you could be in, says how often are you in each one, and how much information is transferred every time you're in one of them.

16:12
Now the question is, okay, well, what is the amount of information in each message then? The way that's calculated is as the negative log of its probability. So that sounds a little bit arbitrary. There are good reasons it's done this way, I'll just try to give a kind of general sense for why this makes sense as a measure of how much information is in a message. So here's the negative log.

16:41
So when something is happens 100% of the time, so when you have a message that is happening 100% of the time, the amount of information in it on this measure is zero. And this should make sense. If something is always in the same state, you don't learn anything when you observe that state. So if the stoplight is always red, and I look at it, and I see its red, I didn't learn anything. So there's no information there. And then the less probable and messages, the more information is carried in it. And this again, should make intuitive sense, a highly improbable message, it surprises you a lot, you learn a lot when you hear a highly improbable message.

17:24
So if I gave you the information "There is a raccoon in my room right now," you'd be learning a lot more than if I said, "There's a cat in my room right now." Because a lot of people have cats in their rooms. (You can you can see that one actually is true. Yes, there is a cat in my room right now). All right.

17:42
So that's the entropy measure. In general, if we hold other aspects fixed, the entropy of any channel is going to be higher when the messages are closer to equiprobable or when there are more messages. And I want to point out that this connects up with these two kinds of cases we talked about when it comes to conventions. So in the Gilbert case, we have scenarios where the evolution of one equilibria is much more likely than the other, or scenarios where they're kind of equally likely. Entropy is going to say... or sorry... the entropy measure will be higher when we have equal likelihood. And with the Milliken example, we had cases where there are more messages more possible equilibria. So entropy is going to be higher, the more messages there are.

18:33
Alright, so just to kind of drive this home, we can use this entropy measure, to say how surprising it is, on average—how much we learn when we observe a particular convention in a society, or when we observe the outcome of a model of cultural evolution. The messages then are these conventional outcomes that have different probabilities of emerging. And then we can say, the higher the entropy, the more arbitrary some arena of evolution is, the more things really could have been otherwise. So returning to this example, if we have this first model where there are two possible outcomes, and they're equally probable, if we calculate the average entropy in this kind of system, it's one. If we move to this other scenario, where we have one very likely outcome, the average entropy in this system is only 0.13 because we usually expect that the b equilibrium evolves, and it does. And so we don't learn that much when we see what actually came out of this system, because there's sort of less randomness in the system.

19:46
All right, so let's talk about what this tells us about conventionality. Once we apply this measure, we can see there's only one value—zero—where the traits emerging in a system like this are not conventional at all. And these are the cases where just one outcome is always guaranteed to emerge. For every other scenario, there's some chance things could have been otherwise. And furthermore, there's no upper bound to this measure, conventions can be arbitrarily arbitrary. And I think that putting this in place really pushes against accounts. And this is what philosophers have almost always done to this point, that want to separate conventions from non conventions. And instead, we should be thinking about the diversity within the category of convention. This also hopefully informs how we explain cultural traits.

20:45
So we generally shouldn't explain cultural traits by appealing only to the functionality of these traits, or only to chance historical factors. Instead, almost every cultural convention is going to be somewhere on this scale, there's going to be some arbitrariness involved in its emergence, but also some payoff reasons or functional reasons or constraints that explain why it emerged.

21:11
All right. So what I'm going to do in wrapping up is talk about three challenges to this account, and then kind of answer these challenges. And then that'll be the end of the talk.

21:22
So challenge one. I just talked about one little type of evolutionary model: Is this framework only applicable to this sort of model? And the answer is absolutely not. We can use any probabilistic representation of the emergence of conventions here. So we can use any kind of cultural evolutionary model where we get multiple possible outcomes. And there are different probabilities of those emerging so we can use infinite population models that have basins of attraction. We can have stochastic models that have different probabilities of outcomes. We can use models that incorporate information about what was the starting point of a population? In what ways was it constrained? Was it influenced by other cultures around it? In addition, we can use real datasets here. So we can look at cross cultural datasets that show across, you know, 400 cultures, here are the different conventions we saw emerging. We can also use things like outcomes and lab experiments where you have groups of individuals learn different conventions, in short time periods. challenge to has to do with representation dependence.

22:32
So of course, for any real case, there are going to be a lot of ways to represent probabilities that different conventions emerge. We can't just observe real probabilities of this in the world, if that's even a thing. Even if we look at data that's not representing some real probability of emergence. It's representing a data set that's been shaped by choices of scientists and all sorts of other probably random factors.

22:58
So that's one issue. Another issue is that when we're talking about the same cultural evolutionary scenarios, there are often different things we might want to measure about them. So we might want to measure arbitrariness or conventionality, absent any kind of context, saying, "forget the fact that real cultures always start somewhere and go somewhere." Imagine that we started from randomness or nowhere. We might want to talk about that. Or we might want to talk about arbitrariness of conventions given a particular set of historical and cultural influences.

23:33
There is no real solution here, I think the best response is that well, representations should be sensitive to the explanatory aims of a project. And they have to be recognised to be imperfect, they always are. So you come up with a best representation that makes sense, given what you're trying to do in some sort of inquiry.

23:55
And the last challenge here, having to do with probabilities. So many people think we live in a deterministic world. And on this picture, there isn't any real sense in which any convention could have been otherwise. But in this case, the fact that we're talking about a measure that depends on a representation actually helps. We represent probabilities however is appropriate for what we're trying to do using models and datasets. And those are the probabilities that we feed into our measure and use to think about how much arbitrariness there is in the process of some convention emerging.

24:29
All right. Alright, so I'll just sum up. conventions come in degrees of arbitrariness, recognising this can improve cultural evolutionary explanation. And for more evidence of that I recommend, check out my paper and look at the examples that I actually draw out there, I give four of them. Second, we can measure this arbitrariness of conventions using information theory. And third, this I didn't elaborate a lot here, but I'll throw in here, this model Measure can actually be used in arguments about the evolution of conventions including things like gender, division of labour and various aspects of human language.

25:09
And with that, I will say "thank you".